Attribute sampling is a method of audit sampling that is used to test the effectiveness of controls by measuring the rate of deviation from a prescribed procedure or attribute. Attribute sampling is suitable for testing compliance with the data center’s physical access log system, as the auditor can compare the identification document numbers and photos of the visitors with the records in the system and determine whether there are any discrepancies or errors. Attribute sampling can also provide an estimate of the deviation rate in the population and allow the auditor to draw a conclusion about the operating effectiveness of the control.

Variable sampling, on the other hand, is a method of audit sampling that is used to estimate the amount or value of a population by measuring a characteristic of interest, such as monetary value, quantity, or size. Variable sampling is not appropriate for testing compliance with the data center’s physical access log system, as the auditor is not interested in estimating the value of the population, but rather in testing whether the system is operating as intended.

Quota sampling and haphazard sampling are both examples of non-statistical sampling methods that do not use probability theory to select a sample. Quota sampling involves selecting a sample based on certain criteria or quotas, such as age, gender, or location. Haphazard sampling involves selecting a sample without any specific plan or method. Both methods are not suitable for testing compliance with the data center’s physical access log system, as they do not ensure that the sample is representative of the population and do not allow the auditor to measure the sampling risk or project the results to the population.

Therefore, attribute sampling is the most useful sampling method for an IS auditor conducting compliance testing for the effectiveness of the data center’s physical access log system.